0.00/0.38	YES
0.00/0.38	
0.00/0.38	Problem 1: 
0.00/0.38	
0.00/0.38	(VAR f g)
0.00/0.38	(THEORY 
0.00/0.38	(AC * +))
0.00/0.38	(RULES
0.00/0.38	dx(*(f,g)) -> +(*(dx(f),g),*(dx(g),f))
0.00/0.38	dx(+(f,g)) -> +(dx(f),dx(g))
0.00/0.38	dx(-(f,g)) -> -(dx(f),dx(g))
0.00/0.38	dx(/(f,g)) -> -(/(dx(f),g),/(*(dx(g),f),exp(g,2)))
0.00/0.38	dx(0) -> 0
0.00/0.38	dx(1) -> 0
0.00/0.38	dx(X) -> 1
0.00/0.38	dx(a) -> 0
0.00/0.38	dx(exp(f,g)) -> +(*(dx(f),*(exp(f,-(g,1)),g)),*(dx(g),*(exp(f,g),ln(f))))
0.00/0.38	dx(ln(f)) -> /(dx(f),f)
0.00/0.38	dx(neg(f)) -> neg(dx(f))
0.00/0.38	)
0.00/0.38	
0.00/0.38	Problem 1: 
0.00/0.38	
0.00/0.38	Dependency Pairs Processor:
0.00/0.38	-> FAxioms:
0.00/0.38	 *#(*(x2,x3),x4) = *#(x2,*(x3,x4))
0.00/0.38	 *#(x2,x3) = *#(x3,x2)
0.00/0.38	 +#(+(x2,x3),x4) = +#(x2,+(x3,x4))
0.00/0.38	 +#(x2,x3) = +#(x3,x2)
0.00/0.38	-> Pairs:
0.00/0.38	 DX(*(f,g)) -> DX(f)
0.00/0.38	 DX(*(f,g)) -> DX(g)
0.00/0.38	 DX(+(f,g)) -> DX(f)
0.00/0.38	 DX(+(f,g)) -> DX(g)
0.00/0.38	 DX(-(f,g)) -> DX(f)
0.00/0.38	 DX(-(f,g)) -> DX(g)
0.00/0.38	 DX(/(f,g)) -> DX(f)
0.00/0.38	 DX(/(f,g)) -> DX(g)
0.00/0.38	 DX(exp(f,g)) -> DX(f)
0.00/0.38	 DX(exp(f,g)) -> DX(g)
0.00/0.38	 DX(ln(f)) -> DX(f)
0.00/0.38	 DX(neg(f)) -> DX(f)
0.00/0.38	-> EAxioms:
0.00/0.38	 *(*(x2,x3),x4) = *(x2,*(x3,x4))
0.00/0.38	 *(x2,x3) = *(x3,x2)
0.00/0.38	 +(+(x2,x3),x4) = +(x2,+(x3,x4))
0.00/0.38	 +(x2,x3) = +(x3,x2)
0.00/0.38	-> Rules:
0.00/0.38	 dx(*(f,g)) -> +(*(dx(f),g),*(dx(g),f))
0.00/0.38	 dx(+(f,g)) -> +(dx(f),dx(g))
0.00/0.38	 dx(-(f,g)) -> -(dx(f),dx(g))
0.00/0.38	 dx(/(f,g)) -> -(/(dx(f),g),/(*(dx(g),f),exp(g,2)))
0.00/0.38	 dx(0) -> 0
0.00/0.38	 dx(1) -> 0
0.00/0.38	 dx(X) -> 1
0.00/0.38	 dx(a) -> 0
0.00/0.38	 dx(exp(f,g)) -> +(*(dx(f),*(exp(f,-(g,1)),g)),*(dx(g),*(exp(f,g),ln(f))))
0.00/0.38	 dx(ln(f)) -> /(dx(f),f)
0.00/0.38	 dx(neg(f)) -> neg(dx(f))
0.00/0.38	-> SRules:
0.00/0.38	 *#(*(x2,x3),x4) -> *#(x2,x3)
0.00/0.38	 *#(x2,*(x3,x4)) -> *#(x3,x4)
0.00/0.38	 +#(+(x2,x3),x4) -> +#(x2,x3)
0.00/0.38	 +#(x2,+(x3,x4)) -> +#(x3,x4)
0.00/0.38	
0.00/0.38	Problem 1: 
0.00/0.38	
0.00/0.38	SCC Processor:
0.00/0.38	-> FAxioms:
0.00/0.38	 *#(*(x2,x3),x4) = *#(x2,*(x3,x4))
0.00/0.38	 *#(x2,x3) = *#(x3,x2)
0.00/0.38	 +#(+(x2,x3),x4) = +#(x2,+(x3,x4))
0.00/0.38	 +#(x2,x3) = +#(x3,x2)
0.00/0.38	-> Pairs:
0.00/0.38	 DX(*(f,g)) -> DX(f)
0.00/0.38	 DX(*(f,g)) -> DX(g)
0.00/0.38	 DX(+(f,g)) -> DX(f)
0.00/0.38	 DX(+(f,g)) -> DX(g)
0.00/0.38	 DX(-(f,g)) -> DX(f)
0.00/0.38	 DX(-(f,g)) -> DX(g)
0.00/0.38	 DX(/(f,g)) -> DX(f)
0.00/0.38	 DX(/(f,g)) -> DX(g)
0.00/0.38	 DX(exp(f,g)) -> DX(f)
0.00/0.38	 DX(exp(f,g)) -> DX(g)
0.00/0.38	 DX(ln(f)) -> DX(f)
0.00/0.38	 DX(neg(f)) -> DX(f)
0.00/0.38	-> EAxioms:
0.00/0.38	 *(*(x2,x3),x4) = *(x2,*(x3,x4))
0.00/0.38	 *(x2,x3) = *(x3,x2)
0.00/0.38	 +(+(x2,x3),x4) = +(x2,+(x3,x4))
0.00/0.38	 +(x2,x3) = +(x3,x2)
0.00/0.38	-> Rules:
0.00/0.38	 dx(*(f,g)) -> +(*(dx(f),g),*(dx(g),f))
0.00/0.38	 dx(+(f,g)) -> +(dx(f),dx(g))
0.00/0.38	 dx(-(f,g)) -> -(dx(f),dx(g))
0.00/0.38	 dx(/(f,g)) -> -(/(dx(f),g),/(*(dx(g),f),exp(g,2)))
0.00/0.39	 dx(0) -> 0
0.00/0.39	 dx(1) -> 0
0.00/0.39	 dx(X) -> 1
0.00/0.39	 dx(a) -> 0
0.00/0.39	 dx(exp(f,g)) -> +(*(dx(f),*(exp(f,-(g,1)),g)),*(dx(g),*(exp(f,g),ln(f))))
0.00/0.39	 dx(ln(f)) -> /(dx(f),f)
0.00/0.39	 dx(neg(f)) -> neg(dx(f))
0.00/0.39	-> SRules:
0.00/0.39	 *#(*(x2,x3),x4) -> *#(x2,x3)
0.00/0.39	 *#(x2,*(x3,x4)) -> *#(x3,x4)
0.00/0.39	 +#(+(x2,x3),x4) -> +#(x2,x3)
0.00/0.39	 +#(x2,+(x3,x4)) -> +#(x3,x4)
0.00/0.39	->Strongly Connected Components:
0.00/0.39	->->Cycle:
0.00/0.39	->->-> Pairs:
0.00/0.39	 DX(*(f,g)) -> DX(f)
0.00/0.39	 DX(*(f,g)) -> DX(g)
0.00/0.39	 DX(+(f,g)) -> DX(f)
0.00/0.39	 DX(+(f,g)) -> DX(g)
0.00/0.39	 DX(-(f,g)) -> DX(f)
0.00/0.39	 DX(-(f,g)) -> DX(g)
0.00/0.39	 DX(/(f,g)) -> DX(f)
0.00/0.39	 DX(/(f,g)) -> DX(g)
0.00/0.39	 DX(exp(f,g)) -> DX(f)
0.00/0.39	 DX(exp(f,g)) -> DX(g)
0.00/0.39	 DX(ln(f)) -> DX(f)
0.00/0.39	 DX(neg(f)) -> DX(f)
0.00/0.39	-> FAxioms:
0.00/0.39	 *(*(x2,x3),x4) -> *(x2,*(x3,x4))
0.00/0.39	 *(x2,x3) -> *(x3,x2)
0.00/0.39	 +(+(x2,x3),x4) -> +(x2,+(x3,x4))
0.00/0.39	 +(x2,x3) -> +(x3,x2)
0.00/0.39	-> EAxioms:
0.00/0.39	 *(*(x2,x3),x4) = *(x2,*(x3,x4))
0.00/0.39	 *(x2,x3) = *(x3,x2)
0.00/0.39	 +(+(x2,x3),x4) = +(x2,+(x3,x4))
0.00/0.39	 +(x2,x3) = +(x3,x2)
0.00/0.39	->->-> Rules:
0.00/0.39	 dx(*(f,g)) -> +(*(dx(f),g),*(dx(g),f))
0.00/0.39	 dx(+(f,g)) -> +(dx(f),dx(g))
0.00/0.39	 dx(-(f,g)) -> -(dx(f),dx(g))
0.00/0.39	 dx(/(f,g)) -> -(/(dx(f),g),/(*(dx(g),f),exp(g,2)))
0.00/0.39	 dx(0) -> 0
0.00/0.39	 dx(1) -> 0
0.00/0.39	 dx(X) -> 1
0.00/0.39	 dx(a) -> 0
0.00/0.39	 dx(exp(f,g)) -> +(*(dx(f),*(exp(f,-(g,1)),g)),*(dx(g),*(exp(f,g),ln(f))))
0.00/0.39	 dx(ln(f)) -> /(dx(f),f)
0.00/0.39	 dx(neg(f)) -> neg(dx(f))
0.00/0.39	-> SRules:
0.00/0.39	 Empty
0.00/0.39	
0.00/0.39	Problem 1: 
0.00/0.39	
0.00/0.39	Subterm Processor:
0.00/0.39	-> FAxioms:
0.00/0.39	 Empty
0.00/0.39	-> Pairs:
0.00/0.39	 DX(*(f,g)) -> DX(f)
0.00/0.39	 DX(*(f,g)) -> DX(g)
0.00/0.39	 DX(+(f,g)) -> DX(f)
0.00/0.39	 DX(+(f,g)) -> DX(g)
0.00/0.39	 DX(-(f,g)) -> DX(f)
0.00/0.39	 DX(-(f,g)) -> DX(g)
0.00/0.39	 DX(/(f,g)) -> DX(f)
0.00/0.39	 DX(/(f,g)) -> DX(g)
0.00/0.39	 DX(exp(f,g)) -> DX(f)
0.00/0.39	 DX(exp(f,g)) -> DX(g)
0.00/0.39	 DX(ln(f)) -> DX(f)
0.00/0.39	 DX(neg(f)) -> DX(f)
0.00/0.39	-> EAxioms:
0.00/0.39	 *(*(x2,x3),x4) = *(x2,*(x3,x4))
0.00/0.39	 *(x2,x3) = *(x3,x2)
0.00/0.39	 +(+(x2,x3),x4) = +(x2,+(x3,x4))
0.00/0.39	 +(x2,x3) = +(x3,x2)
0.00/0.39	-> Rules:
0.00/0.39	 dx(*(f,g)) -> +(*(dx(f),g),*(dx(g),f))
0.00/0.39	 dx(+(f,g)) -> +(dx(f),dx(g))
0.00/0.39	 dx(-(f,g)) -> -(dx(f),dx(g))
0.00/0.39	 dx(/(f,g)) -> -(/(dx(f),g),/(*(dx(g),f),exp(g,2)))
0.00/0.39	 dx(0) -> 0
0.00/0.39	 dx(1) -> 0
0.00/0.39	 dx(X) -> 1
0.00/0.39	 dx(a) -> 0
0.00/0.39	 dx(exp(f,g)) -> +(*(dx(f),*(exp(f,-(g,1)),g)),*(dx(g),*(exp(f,g),ln(f))))
0.00/0.39	 dx(ln(f)) -> /(dx(f),f)
0.00/0.39	 dx(neg(f)) -> neg(dx(f))
0.00/0.39	-> SRules:
0.00/0.39	 Empty
0.00/0.39	->Projection:
0.00/0.39	 pi(DX) = [1]
0.00/0.39	
0.00/0.39	Problem 1: 
0.00/0.39	
0.00/0.39	SCC Processor:
0.00/0.39	-> FAxioms:
0.00/0.39	 Empty
0.00/0.39	-> Pairs:
0.00/0.39	 Empty
0.00/0.39	-> EAxioms:
0.00/0.39	 *(*(x2,x3),x4) = *(x2,*(x3,x4))
0.00/0.39	 *(x2,x3) = *(x3,x2)
0.00/0.39	 +(+(x2,x3),x4) = +(x2,+(x3,x4))
0.00/0.39	 +(x2,x3) = +(x3,x2)
0.00/0.39	-> Rules:
0.00/0.39	 dx(*(f,g)) -> +(*(dx(f),g),*(dx(g),f))
0.00/0.39	 dx(+(f,g)) -> +(dx(f),dx(g))
0.00/0.39	 dx(-(f,g)) -> -(dx(f),dx(g))
0.00/0.39	 dx(/(f,g)) -> -(/(dx(f),g),/(*(dx(g),f),exp(g,2)))
0.00/0.39	 dx(0) -> 0
0.00/0.39	 dx(1) -> 0
0.00/0.39	 dx(X) -> 1
0.00/0.39	 dx(a) -> 0
0.00/0.39	 dx(exp(f,g)) -> +(*(dx(f),*(exp(f,-(g,1)),g)),*(dx(g),*(exp(f,g),ln(f))))
0.00/0.39	 dx(ln(f)) -> /(dx(f),f)
0.00/0.39	 dx(neg(f)) -> neg(dx(f))
0.00/0.39	-> SRules:
0.00/0.39	 Empty
0.00/0.39	->Strongly Connected Components:
0.00/0.39	 There is no strongly connected component
0.00/0.39	
0.00/0.39	The problem is finite.
0.00/0.39	EOF